A bullet of mass 20g is fired from a riffle of mass 8kg with a velocity of $100\text{\hspace{0.17em}m/s.}$ The velocity of recoil of the riffle is

${\text{m}}_{\text{1}}=20\text{\hspace{0.17em}g}=0.02\text{\hspace{0.17em}kg}$

${\text{u}}_1=0\text{\hspace{0.17em}m/s}$

${\text{v}}_1=100{\text{\hspace{0.17em}m/s\hspace{0.17em},\hspace{0.17em}v}}_{\text{2}}=?$

Using conservation of linear momentum

${\text{m}}_{\text{1}}{\text{u}}_{\text{1}}+{\text{m}}_{\text{2}}{\text{u}}_{\text{2}}={\text{m}}_{\text{1}}{\text{v}}_{\text{1}}+{\text{m}}_{\text{2}}{\text{v}}_{\text{2}}$

$0+0=0.02\times 100+8\times {\text{v}}_{\text{2}}$

$=\frac{2}{100}\times 100+8{\text{v}}_{\text{2}}$

$=2+8{\text{v}}_{\text{2}}$

$-2=8{\text{v}}_{\text{2}}$

$\frac{-2}{8}={\text{v}}_{\text{2}}$

$\frac{-1}{4}={\text{v}}_{\text{2}}$

${\text{v}}_{\text{2}}=-0.25\text{\hspace{0.17em}m/s}$